Hydrodynamic interactions between widely separated particles at a free surfaceB. Cichocki1, M. L. Ekiel-Jezewska2, G. Nägele3 and E. Wajnryb2
1 Institute of Theoretical Physics, Warsaw University Hoza 69, 00-618 Warsaw, Poland
2 Institute of Fundamental Technological Research, Polish Academy of Sciences Swietokrzyska 21, 00-049 Warsaw, Poland
3 Institut für Festkörperforschung, Soft Matter Division, Forschungszentrum Jülich D-52425 Jülich, Germany
(Received 13 April 2004; accepted in final form 24 May 2004)
In this letter, we consider a quasi-two-dimensional (Q2D) system of widely separated spheres suspended in a quiescent fluid and in contact with a planar fluid-gas interface. We construct and estimate the accuracy of two generic approximations to the translational-translational mobility, needed, e.g., in Brownian simulations. Both simplifications for Q2D systems are shown to be essentially different than their three-dimensional well-known analogs. First, we discuss the asymptotic form of the Q2D two-sphere mobility up to cubic order in the inverse inter-particle distance and compare it with the corresponding three-dimensional Rotne-Prager expression. We also explain how to avoid divergences due to lubrication forces at the contact. Next, we construct the Q2D mobility of point-particles, which -unlike in 3D- is not pairwise additive. Finally, we determine the range of validity of both long-distance approximations by computing numerically exact results.
47.15.Gf - Low-Reynolds-number (creeping) flows.
82.70.-y - Disperse systems; complex fluids.
© EDP Sciences 2004